A `3 kg` block of wood is on a level surface where `mu_(s) = 0.25` and `mu_(s) = 0.2 `A force of `7 N` is being applied horizontal to the block Mark the correct statement(s) regarding this situation.

Options

A. If the block is initially at rest , it will remain at rest and friction force will be about ?`7 N`
B. If the block is initially moving than it will continue its motion forever if the force applies is in the direction of the motion of the block
C. If the block is initially moving and the direction of applied force is mass as that of motion of block , than block moves with an acceleration of `1//3 ms^(-2)` along its initial direction of motion
D. If the block is initially moving and direction of applied force to that of initial motion of the blockthan the block decelerates comes to a stop and starts moving in the opposite direction.

Answer

a,b,c

Explanation

If the block is at rest force applied has to be greater than limiting friction force for the its motion to begain
`f_(1) = mu_(s) mg = 0.25 xx 3 g = 7.5 N lt f_(applied)`
So friction is static in nature and its value would be equal to applied force i.e. `7 N` If the body is initially moving then kinetic friction is present `(f_(k) mu_(k) = 6N)` , acting , then opposite to direction of motion .
`As F gt f_(k)` the block is acceleration with an acceleration of
`a = [(F - f_(k))/(m)] = (1)/(3) ms^(-2)` and hence its speed contimonously increasing
If applied force is opposite direction of motion , then block is under deceleration of `a = [(F + f_(k))/(m)] = (13)/(3)ms^(-2)` and hence after some time block stope and kinetic friction venishes but applied force contimes ti act
But as `F lt f_(2)` the block remain at rest and friction force acquires the value equal to applied force, i.e. friction is static in nature